A company publishes statistics concerning car quality. The initial quality score

Question

A company publishes statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For one year, Car A had 1.18 problems per car. Let the random variable X be equal to the number of problems with a newly purchased model A car. Complete (a) and (b) below. If you purchased a model A car, what is the probability that the new car will have zero problems? The probability that the new model A car will have zero problems is (Round to four decimal places as needed.) If you purchased a model A car, what is the probability that the new car will have two or fewer problems? The probability that a new model A car will have two or fewer problems is (Round to four decimal places as needed.)

Explanation / Answer

= 1.18

This is a poisson distribution

P(X = x) = e- * x / x!

a) P(X = 0) = e-1.18 * 1.180 / 0!

                  = 0.3073

b) P(X < 2) = P(X = 0) + P(X = 1) + P(X = 2)

                  = e-1.18 * 1.180 / 0! + e-1.18 * 1.181 / 1! + e-1.18 * 1.182 / 2!

                 = 0.8838

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